Consensus Control of a Multi-Agent Rigid Body System on TSO(3)N and TSE(3)N

Nonlinear control laws are proposed for consensus control of a multi-agent system of N heterogeneous rigid bodies in the framework of the tangent bundles TSO (3) and TSE (3) associated with Lie groups SO (3) and SE (3). The control objective is to stabilize the relative pose configurations with velocity synchronization of the rigid bodies which share their states according to a static communication topology. The feedback control design is conducted on the dynamic level in which masses and inertias are not negligible and uses the rotation matrix as opposed to various attitude parameterizations. Almost global asymptotic stability of the consensus subspace is demonstrated both analytically and through numerical simulations.